Differentials, taylor series, and function notation

"Expanding the taylor series for ##f(x)##.." (See picture) is this a typo? Aren't we expanding ##f(x + \Delta x)##?

Also, when we evaluate ##f(x)## (coefficients in the expansion), are we assuming ##\Delta x = 0## by setting ##x + \Delta x## (argument of the function) equal to ##x##? Or are we...



Differentials, taylor series, and function notation

Differentials, taylor series, and function notation